Question: Divide the following complex numbers: $\dfrac{8(\cos(\frac{5}{3}\pi) + i \sin(\frac{5}{3}\pi))}{\cos(\frac{1}{3}\pi) + i \sin(\frac{1}{3}\pi)}$ (The dividend is plotted in blue and the divisor in plotted in green. Your current answer will be plotted orange.)
Solution: Dividing complex numbers in polar forms can be done by dividing the radii and subtracting the angles. The first number ( $8(\cos(\frac{5}{3}\pi) + i \sin(\frac{5}{3}\pi))$ ) has angle $\frac{5}{3}\pi$ and radius 8. The second number ( $\cos(\frac{1}{3}\pi) + i \sin(\frac{1}{3}\pi)$ ) has angle $\frac{1}{3}\pi$ and radius 1. The radius of the result will be $\frac{8}{1}$ , which is 8. The angle of the result is $\frac{5}{3}\pi - \frac{1}{3}\pi = \frac{4}{3}\pi$ The radius of the result is $8$ and the angle of the result is $\frac{4}{3}\pi$.